
is satisfied.
Writing a solution \((X,r)\)  as \(r\left(x,y\right) = \left(\lambda _x\left(y\right)\rho _y\left(x\right)\right)\) , with
\(\lambda _x, \rho _x\)  maps from \(X\)  into itself, for every \(x\in X\) , we say that \((X, r)\)  is left non-degenerate if \(\lambda _x\in \operatorname{Sym}_X\)  for every \(x\in X\) , non-degenerate if \(\lambda _x,\rho _x \in \operatorname{Sym}_X\)  for every \(x\in X\) , and involutive if \(r^2=\operatorname{id}_{X\times X}\) .
After the seminal papers of Gateva-Ivanova and Van den Bergh [1]}, Gateva-Ivanova and Majid [2]}, and Etingov, Schedler, and Soloviev [3]}, the involutive non-degenerate solutions have been widely studied.
